Modi, who arrived in Glasgow on Sunday night from Rome, was received by Johnson and UN Secretary General Antonio Guterres and was then seen interacting animatedly with them.
The three leaders also attended the G20 Summit in Italy which concluded on Sunday.
“Together for our planet! PM @narendramodi received by UK PM @BorisJohnson and UN Secretary General @antonioguterres as he arrives at the Scottish Exhibition Centre to attend the World Leaders Summit of @COP26,” Ministry of External Affairs (MEA) spokesperson Arindam Bagchi tweeted.
Later, Johnson opened the climate summit, warning that two degrees more to global temperatures will jeopardise food supplies, three degrees more will bring more wildfires and cyclones, while four degrees and “we say goodbye to whole cities”.
He made the comparison between world leaders and James Bond, saying that the fictional secret agent often ends his films fighting to stop a force from ending the world.
“The tragedy is that this is not a movie and the doomsday device is real,” he warned.
During the high-profile segment of the World Leaders’ Summit, Prime Minister Modi will be presenting the formal position on India’s climate action agenda and lay out the best practices and achievements in the sector at the COP26 summit.
At the end of day one of the World Leaders’ Summit on Monday, Modi will join more than 120 Heads of Government and Heads of State at a special VVIP reception at Kelvingrove Art Gallery and Museum – one of Scotland’s most popular visitor attractions.
The reception will also involve members of the royal family, including Prince Charles and wife Camilla and Prince William and wife Kate Middleton.
Queen Elizabeth II was due to attend this special reception but pulled out last week after a medical advice against travel.